A Michigan study concerning preference for outdoor activities used a questionnaire with a six-point Likert-type response in which 1 designated "not important" and 6 designated "extremely important." A random sample of n1 = 49 adults were asked about fishing as an outdoor activity. The mean response was x1 = 4.9. Another random sample of n2 = 45 adults were asked about camping as an outdoor activity. For this group, the mean response was x2 = 4.2. From previous studies, it is known that σ1 = 1.3 and σ2 = 1.2. Does this indicate a difference (either way) regarding preference for camping versus preference for fishing as an outdoor activity? Use a 10% level of significance.
Note: A Likert scale usually has to do with approval of or agreement with a statement in a questionnaire. For example, respondents are asked to indicate whether they "strongly agree," "agree," "disagree," or "strongly disagree" with the statement.
(a) What is the level of significance?
What is the value of the sample test statistic? (Use 2 decimal places.)
(c) Find (or estimate) the P-value. (Use 4 decimal places.)
Education influences attitude and lifestyle. Differences in education are a big factor in the "generation gap." Is the younger generation really better educated? Large surveys of people age 65 and older were taken in n1 = 36 U.S. cities. The sample mean for these cities showed that x1 = 15.2% of the older adults had attended college. Large surveys of young adults (age 25 - 34) were taken in n2 = 39 U.S. cities. The sample mean for these cities showed that x2 = 19.2% of the young adults had attended college. From previous studies, it is known that σ1 = 7.4% and σ2 = 5.4%. Does this information indicate that the population mean percentage of young adults who attended college is higher? Use α = 0.05.
(a) What is the level of significance?
What is the value of the sample test statistic? (Test the difference μ1 - μ2. Round your answer to two decimal places.)
(c) Find (or estimate) the P-value. (Round your answer to four decimal places.)
In the journal Mental Retardation, an article reported the results of a peer tutoring program to help mildly mentally retarded children learn to read. In the experiment, the mildly retarded children were randomly divided into two groups: the experimental group received peer tutoring along with regular instruction, and the control group received regular instruction with no peer tutoring. There were n1 = n2 = 41 children in each group. The Gates-MacGintie Reading Test was given to both groups before instruction began. For the experimental group, the mean score on the vocabulary portion of the test was x1 = 344.5, with sample standard deviation s1 = 43.2. For the control group, the mean score on the same test was x2 = 328.7, with sample standard deviation s2 = 43.4. Use a 1% level of significance to test the hypothesis that there was no difference in the vocabulary scores of the two groups before the instruction began.
(a) What is the level of significance?
What is the value of the sample test statistic? (Use 3 decimal places.)
(c) Find (or estimate) the P-value. (Use 4 decimal places.)
In the journal Mental Retardation, an article reported the results of a peer tutoring program to help mildly mentally retarded children learn to read. In the experiment, Form 2 of the Gates-MacGintie Reading Test was administered to both an experimental group and a control group after 6 weeks of instruction, during which the experimental group received peer tutoring and the control group did not. For the experimental group n1 = 41 children, the mean score on the vocabulary portion of the test was x1 = 368.4, with sample standard deviation s1 = 42.8. The average score on the vocabulary portion of the test for the n2 = 41 subjects in the control group was x2 = 348.4 with sample standard deviation s2 = 50.0. Use a 5% level of significance to test the claim that the experimental group performed better than the control group.
(a) What is the level of significance?
What is the value of the sample test statistic? (Round your answer to three decimal places.)
(c) Find (or estimate) the P-value. (Round your answer to four decimal places.)